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Time-Dependent Monoenergetic Neutron Transport in Two Adjacent Semi-infinite Media


Erdmann, Robert Charles (1966) Time-Dependent Monoenergetic Neutron Transport in Two Adjacent Semi-infinite Media. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/00R6-9A13.


An exact solution to the monoenergetic Boltzmann equation is obtained for the case of a plane isotropic burst of neutrons introduced at the interface separating two adjacent, dissimilar, semi-infinite media. The method of solution used is to remove the time dependence by a Laplace transformation, solve the transformed equation by the normal mode expansion method, and then invert to recover the time dependence.

The general result is expressed as a sum of definite, multiple integrals, one of which contains the uncollided wave of neutrons originating at the source plane. It is possible to obtain a simplified form for the solution at the interface, and certain numerical calculations are made there.

The interface flux in two adjacent moderators is calculated and plotted as a function of time for several moderator materials. For each case it is found that the flux decay curve has an asymptotic slope given accurately by diffusion theory. Furthermore, the interface current is observed to change directions when the scattering and absorption cross sections of the two moderator materials are related in a certain manner. More specifically, the reflection process in two adjacent moderators appears to depend initially on the scattering properties and for long times on the absorption properties of the media.

This analysis contains both the single infinite and semi-infinite medium problems as special cases. The results in these two special cases provide a check on the accuracy of the general solution since they agree with solutions of these problems obtained by separate analyses.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Applied Mechanics and Physics)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Mechanics
Minor Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Lurie, Harold
Thesis Committee:
  • Unknown, Unknown
Defense Date:27 July 1965
Record Number:CaltechTHESIS:10022015-101429428
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9192
Deposited By: Benjamin Perez
Deposited On:02 Oct 2015 22:19
Last Modified:28 Feb 2024 00:53

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